Answer :

If the direction ratios of two lines segments are proportional, then the lines are collinear.

Given A(2, 3, 4), B(−1, −2, 1), C(5, 8, 7)


Direction ratio of line joining A (2,3,4) and B (−1, −2, 1), are


(−1−2), (−2−3), (1−4)


= (−3, −5, −3)


So a1 = -3, b1 = -5, c1 = -3


Direction ratio of line joining B (−1, −2, 1) and C (5, 8, 7) are


(5− (−1)), (8−(−2)), (7−1)


= (6, 10, 6)


So a2 = 6, b2 = 10 and c2 =6


It is clear that the direction ratios of AB and BC are of same proportions


As




and



Therefore A, B, C are collinear.


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